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Thermodynamics



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Chapter 6 : Thermodynamics



6.0 Thermodynamics arrow_upward


  • Thermodynamic is the study of effect of the HEAT, WORK and ENERGY on a system.

  • 6.1 Thermodynamic Terms arrow_upward


  • Chemical reactions and the energy changes accompanying them. For this we need to know certain thermodynamic terms.

  • 6.1.1 The System and the Surroundings

  • A system in thermodynamics refers to that part of universe in which observations are made and remaining universe constitutes the surroundings. The surroundings include everything other than the system. System and the surroundings together constitute the universe.
  • The universe = the system + the surroundings


    6.1.2 Types of the System

    Open System:
  • In an open system, there is exchange of energy and matter between system and surroundings. The presence of reactants in an open beaker is an example of an open system.
  • Closed System:
  • In a closed system, there is no exchange of matter, but exchange of energy is possible between system and the surroundings.
  • The presence of reactants in a closed vessel made of conducting material e.g., copper or steel is an example of a closed system.
  • Isolated System:
  • In an isolated system, there is no exchange of energy or matter between the system and the surroundings.
  • The presence of reactants in a thermos flask or any other closed insulated vessel is an example of an isolated system.

  • 6.1.3 The State of the System

  • The state of a thermodynamic system is described by its measurable or macroscopic (bulk) properties.
  • The state of a gas is defined by quoting its pressure (p), volume (V), temperature (T), amount (n) etc.
  • Variables like p, V, T are called state variables or state functions because their values depend only on the state of the system and not on how it is reached.
  • In order to completely define the state of a system it is not necessary to define all the properties of the system; as only a certain number of properties can be varied independently.

  • 6.1.4 The Internal Energy as a State Function

  • Internal Energy represents the total energy (chemical, electrical, mechanical) of the system. Internal Energy may change when,
    • Heat passes into or out of the system,
    • Work is done on or by the system,
    • Matter enters or leaves the system.
    Work:
  • Take a system containing some quantity of water in a thermos flask or in an insulated beaker. This would not allow exchange of heat between the system and surroundings through its boundary and we call this type of system as adiabatic.
  • Adiabatic process:
    • Adiabatic process is a process in which there is no transfer of heat between the system and surroundings.
  • In the figure given below the wall separating the system and the surroundings is called the adiabatic wall.
  • Let us bring the change in the internal energy of the system by doing some work on it. Let us call the initial state of the system as state A and its temperature as TA .
  • Let the internal energy of the system in state A be called UA . We can change the state of the system in two different ways.
    • One way: We do some mechanical work, say 1 kJ, by rotating a set of small paddles and thereby churning water. Let the new state be called B state and its temperature, as TB . It is found that TB > TA and the change in temperature, = TB – TA .
    • Second way: We now do an equal amount (i.e., 1kJ) electrical work with the help of an immersion rod and note down the temperature change. We find that the change in temperature is same i.e., TB – TA .
  • Now we will define the internal energy U, whose value is characteristic of the state of a system, whereby the adiabatic work, wad required to bring about a change of state is equal to the difference between the value of U in one state and that in another state,  i.e.,
  •                         

  • Therefore, internal energy, U, of the system is a state function.
  • Heat:
  • The internal energy of a system can also be changed by transfer of heat from the surroundings to the system or vice-versa without expenditure of work. This exchange of energy, which is a result of temperature difference is called heat, q.
  • Consider a system which allows heat transfer through its boundary.
  • Take water at temperature, TA in a container having thermally conducting walls, say made up of copper and enclose it in a huge heat reservoir at temperature, TB . The heat absorbed by the system (water), q can be measured in terms of temperature difference, TB – TA . In this case change in internal energy, , when no work is done at constant volume.
  • The q is positive, when heat is transferred from the surroundings to the system and q is negative when heat is transferred from system to the surroundings.
  • The general case:
  • Consider the general case in which a change of state is brought about both by doing work and by transfer of heat. We write change in internal energy for this case as:
  • This equation is the mathematical statement of the first law of thermodynamics, which states that
  • “The energy of an isolated system is constant.”


    6.2 Applications arrow_upward


  • Chemical reactions involve the generation of gases capable of doing mechanical work or the generation of heat.

  • 6.2.1 Work

  • Mechanical work i.e., pressure-volume work.
  • In thermodynamics system work performed on two processes:
    • Reversible process
    • Irreversible process
    1. Reversible process
  • A process that can be "reversed" by means of infinitesimal changes in some property of the system without entropy production.
  • 2. Irreversible process
  • A change in the thermodynamic state of a system and all of its surroundings cannot be precisely restored to its initial state by infinitesimal changes in some property of the system without expenditure of energy.

  • 6.2.2 Enthalpy, H arrow_upward


  • The heat absorbed at constant volume is equal to change in the internal energy i.e.,
  • Heat absorbed at constant pressure is:
  • Enthalpy H is defined as:
  • H = U + pV

  • H is a state function because it depends on U, p and V, all of which are state functions.
  • a) A useful new state function
  • At constant pressure:
  • Since p is constant, we can write
  •  ------ (1)

     is negative for exothermic reactions which evolve heat during the reaction and  is positive for endothermic reactions which absorb heat from the surroundings.

     qp , heat absorbed by the system at constant pressure.

  • At constant volume  , therefore equation (1) becomes
  • (b) Extensive and Intensive Properties
  • An extensive property is a property whose value depends on the quantity or size of matter present in the system. For example, mass, volume, internal energy, enthalpy, heat capacity, etc.
  • Those properties which do not depend on the quantity or size of matter present are known as intensive properties. For example temperature, density, pressure etc. are intensive properties.
  • (c) Heat Capacity
  • The increase of temperature is proportional to the heat transferred.
  • The coefficient, C is called the heat capacity.
  • The magnitude of the coefficient depends on the size, composition and nature of the system.
  • When C is large, a given amount of heat results in only a small temperature rise.
  • C is directly proportional to amount of substance. The molar heat capacity of a substance,  is the heat capacity for one mole of the substance and is the quantity of heat needed to raise the temperature of one mole by one degree celsius (or one kelvin).
  • (b) Extensive and Intensive Properties
  • An extensive property is a property whose value depends on the quantity or size of matter present in the system. For example, mass, volume, internal energy, enthalpy.
  • Those properties which do not depend on the quantity or size of matter present are known as intensive properties. For example temperature, density, pressure etc. are intensive properties.
  • (c) Specific Heat
  • Specific heat, also called specific heat capacity is the quantity of heat required to raise the temperature of one unit mass of a substance by one degree Celsius (or one kelvin). For finding out the heat, q, required to raise the temperatures of a sample, we multiply the specific heat of the substance, c, by the mass m, and temperatures change, ΔT as
  • (d) The Relationship between Cp and CV for an ideal gas
  • At constant volume, the heat capacity, C is denoted by CV and at constant pressure, this is denoted by Cp .
    • At constant volume:

    • At constant pressure:

  • The difference between Cp and CV can be derived for an ideal gas as:
  •     For a mole of an ideal gas,

           

           

           

  • On putting the values of  and , we have
  •        


    6.3 Measurement Of  and : Calorimetry arrow_upward


  • Calorimetry is an experimental technique that measure energy changes associated with chemical or physical processes.
  • The process is carried out in a vessel called calorimeter, which is immersed in a known volume of a liquid.
  • Knowing the heat capacity of the liquid in which calorimeter is immersed and the heat capacity of calorimeter, it is possible to determine the heat evolved in the process by measuring temperature changes.
  • Measurements are made under two different conditions:
    • At constant volume, qV
    • At constant pressure, qp
    (a)  Measurements
    Bomb Calorimeter:
  • For chemical reactions, heat absorbed at constant volume, is measured in a bomb calorimeter.
  • Here, a steel vessel (the bomb) is immersed in a water bath. The whole device is called calorimeter.
  • The steel vessel is immersed in water bath to ensure that no heat is lost to the surroundings. A combustible substance is burnt in pure dioxygen supplied in the steel bomb.
  • Heat evolved during the reaction is transferred to the water around the bomb and its temperature is monitored. Since the bomb calorimeter is sealed, its volume does not change i.e., the energy changes associated with reactions are measured at constant volume.
  • Under these conditions, no work is done as the reaction is carried out at constant volume in the bomb calorimeter. Even for reactions involving gases, there is no work done as .
  • Temperature change of the calorimeter produced by the completed reaction is then converted to qV, by using the known heat capacity of the calorimeter with the help of equation
  • (b)  Measurements
  • Measurement of heat change at constant pressure (generally under atmospheric pressure) can be done in a calorimeter
  • In an exothermic reaction, heat is evolved, and system loses heat to the surroundings. Therefore, qp will be negative and  will also be negative. Similarly in an endothermic reaction, heat is absorbed, qp is positive and   will be positive.

  • 6.4 Enthalpy Change,  of a Reaction – Reaction Enthalpy arrow_upward


  •  In a chemical reaction, reactants are converted into products and is represented by,
  •    

  • The enthalpy change accompanying a reaction is called the reaction enthalpy. The enthalpy change of a chemical reaction is given by the symbol.
  • (Here symbol  (sigma) is used for summation and ai and bi are the stoichiometric coefficients of the products and reactants respectively.
  • (a) Standard enthalpy of reactions
  • The standard enthalpy of reaction is the enthalpy change for a reaction when all the participating substances are in their standard states.
  • The standard state of a substance at a specified temperature is its pure form at 1 bar.
  • (b) Enthalpy changes during phase transformations
  • The enthalpy change that accompanies melting of one mole of a solid substance in standard state is called standard enthalpy of fusion or molar enthalpy of fusion,
  •  is enthalpy of fusion in standard state.

  • Amount of heat required to vaporize one mole of a liquid at constant temperature and under standard pressure (1bar) is called its standard enthalpy of vaporization or molar enthalpy of vaporization,
  •  is the standard enthalpy of vaporization.

    (c) Standard enthalpy of formation
  • The standard enthalpy change for the formation of one mole of a compound from its elements in their most stable states of aggregation (also known as reference states) is called Standard Molar Enthalpy of Formation. Its symbol is .
  • (d) Thermochemical equations
  • A balanced chemical equation together with the value of its  is called a thermochemical equation.
  • Example:

  • The above equation describes the combustion of liquid ethanol at constant temperature and pressure. The negative sign of enthalpy change indicates that this is an exothermic reaction.
  • Note:
  • The coefficients in a balanced thermochemical equation refer to the number of moles (never molecules) of reactants and products involved in the reaction.
  • The numerical value of  refers to the number of moles of substances specified by an equation. Standard enthalpy change  will have units as kJ mol-1 .
  • (e) Hess’s Law of Constant Heat Summation
  • Hess’ Law can be stated be as follows:
    • “If a reaction takes place in several steps then its standard reaction enthalpy is the sum of the standard enthalpies of the intermediate reactions into which the overall reaction may be divided at the same temperature.”
  • In general, if enthalpy of an overall reaction  along one route is  and  ..... representing enthalpies of reactions leading to same product, B along another route, then we have
  • It can be represented as:

  • 6.5 Enthalpies for different types of Reactions arrow_upward


  • There are different types of enthalpies and reaction:
  • (a) Standard enthalpy of combustion (symbol : )
  • Combustion reactions are exothermic in nature. Standard enthalpy of combustion is defined as
    • “The enthalpy change per mole (or per unit amount) of a substance, when it undergoes combustion and all the reactants and products being in their standard states at the specified temperature.”
    Example:
  • Cooking gas in cylinders contains mostly butane (C4 H10 ). During complete combustion of one mole of butane, 2658 kJ of heat is released.
  • (b) Enthalpy of atomization (symbol:)
  • Consider the following example of atomization of dihydrogen
  • H atoms are formed by breaking H-H bonds in dihydrogen. The enthalpy change in this process is known as enthalpy of atomization, .
  • It is the enthalpy change on breaking one mole of bonds completely to obtain atoms in the gas phase.
  • In case of diatomic molecules, like dihydrogen, the enthalpy of atomization is also the bond dissociation enthalpy.
  • (c) Bond Enthalpy (symbol:)
  • Chemical reactions involve the breaking and making of chemical bonds. Energy is required to break a bond and energy is released when a bond is formed.
  • With reference to the enthalpy changes associated with chemical bonds, two different terms are used in thermodynamics.
    • Bond dissociation enthalpy
    • Mean bond enthalpy
    Bond dissociation enthalpy:
  • The bond dissociation enthalpy is the change in enthalpy when one mole of covalent bonds of a gaseous covalent compound is broken to form products in the gas phase.
  • it is the same as the enthalpy of atomization of dihydrogen. This is true for all diatomic molecules. For example:
  • Mean bond enthalpy:
  • Consider a polyatomic molecule like methane, CH4 .
  • In methane, all the four C - H bonds are identical in bond length and energy. However, the energies required to break the individual C - H bonds in each successive step differ:
  • In such cases we use mean bond enthalpy of C – H bond.
  • Mean C – H bond enthalpy in methane is 416 kJ/mol.
  • (d) Enthalpy of Solution (symbol)
  • Enthalpy of solution of a substance is the enthalpy change when one mole of it dissolves in a specified amount of solvent.
  • The enthalpy of solution at infinite dilution is the enthalpy change observed on dissolving the substance in an infinite amount of solvent when the interactions between the ions (or solute molecules) are negligible.
  • When an ionic compound dissolves in a solvent, the ions leave their ordered positions on the crystal lattice. These are now more free in solution. But solvation of these ions (hydration in case solvent is water) also occurs at the same time.
  • The enthalpy of solution of AB(s), , in water is, therefore, determined by the selective values of the lattice enthalpy,  and enthalpy of hydration of ions,  as

  • Lattice Enthalpy:

  • The lattice enthalpy of an ionic compound is the enthalpy change which occurs when one mole of an ionic compound dissociates into its ions in gaseous state.
  • Born-Haber Cycle:
  • To calculate the lattice enthalpy of Na+ Cl- (s), follow these steps:
  •  

  • Step 1:
  • , sublimation of sodium metal,

  • Step 2:
  •  the ionization of sodium atoms, ionization enthalpy

  • Step 3:
  •  The dissociation of chlorine, the reaction enthalpy is half the bond enthalpy.

  • Step 4:
  • Cl (g) + e-1 (g)  Cl-1 (g) electron gained by chlorine atoms. The electron gained enthalpy,

  • Step 5:
  • Na+ (g) + Cl- (g)  Na+ Cl- (s)

  • The importance of the cycle is that, the sum of the enthalpy changes round a cycle is zero.
  • Applying Hess’s Law, we get,

         For one mole of NaCl(s), lattice enthalpy = 788 kJ mol-1 and 

    = +4 kJ mol-1


    6.6 Spontaneity arrow_upward


  • Spontaneous reaction is one which occurs immediately when contact is made between the reactants.
  • Spontaneity means ‘having the potential to proceed without the assistance of external agency’.
  • A spontaneous process is an irreversible process and may only be reversed by some external agency.
  • (a) Is decrease in enthalpy a criterion for spontaneity?
  • Consider the following equation:
  • The decrease in enthalpy in passing from reactants to products may be shown for any exothermic reaction on an enthalpy diagram as shown in the figure given below:
  • Consider the following equation:
  • These reactions though endothermic, are spontaneous. The increase in enthalpy may be represented on an enthalpy diagram as shown in the figure given below:
  • Therefore, it becomes obvious that while decrease in enthalpy may be a contributory factor for spontaneity, but it is not true for all cases.
  • (b)  Entropy and spontaneity
  • Consider diffusion of two gases into each other in a closed container which is isolated from the surroundings.
  • The two gases, say, gas A and gas B are represented by black dots and white dots respectively and separated by a movable partition. When the partition is withdrawn, the gases begin to diffuse into each other and after a period of time, diffusion will be complete.
  • In an isolated system, there is always a tendency for the systems’ energy to become more disordered or chaotic and this could be a criterion for spontaneous change.
  • Entropy is defined as a measure of the degree of randomness or disorder in the system and is denoted as S.
  • The greater the disorder in an isolated system, the higher is the entropy.
  • Entropy is a state function and  is independent of path.
  •  is related with q and T for a reversible reaction as:

  • The total entropy change  for the system and surroundings of a spontaneous process is given by:
  • When a system is in equilibrium, the entropy is maximum, and the change in entropy, .
  • (c)  Gibbs energy and spontaneity
  • Gibbs Function is defined as:
  • G = H – TS

  • Gibbs function, G is an extensive property and a state function.
  • The change in Gibbs energy for the system,  can be written as:
  • At constant temperature,
  • Thus, Gibbs equation is given as:
  •     Gibbs Energy Change = Enthalpy Change – Temperature × Entropy Change

  • As  is the net energy available to do useful work, it is thus a measure of the free energy. For this reason, it is also known as the free energy of the reaction.
  •  Gives a criteria for spontaneity at constant pressure and temperature:

  • If  is negative (< 0), the process is spontaneous.
  • If  is positive (> 0), the process is non – spontaneous.

  • 6.7 Gibbs Energy Change and Equilibrium arrow_upward


  • The criterion for equilibrium is:
  • Gibbs energy for a reaction in which all reactants and products are in standard state,  is related to the equilibrium constant of the reaction as follows:
  • Or

    Or

    We also know that,

  • For strongly endothermic reactions, the value of  may be large and positive. In such a case, value of K will be much smaller than 1 and the reaction is unlikely to form much product.
  • In case of exothermic reactions,  is large and negative, and  is likely to be large and negative too. In such cases, K will be much larger than 1.
  •  



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